Question

The probability of happening of an impossible event that is, $P\left(\phi \right)$ is

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is B

$0$

Explanation for correct option:

The probability of an impossible event is $P\left(\phi \right)$

The probability of an event which is not possible is always $0$

Therefore $P\left(\phi \right)=0$.

For instance, If we roll a fair die, the possibility is that you will get a number not more than $6$. There is a possibility of getting outcome $1,2,3,4,5$or $6$. Here, outcome $9$ or any number greater than $6$ is an impossible outcome, not included in sample space. Thus, we can conclude that the probability of an impossible event is $0$.

The likelihood that an event won't happen at all or that it won't have any chance of happening in the future is known as the probability of an impossible occurrence.

Therefore the probability of impossible event that is $P\left(\phi \right)=0$

Hence, option (B) is correct